where \(P\)  is the dissipation power and A is the area of the channel, indicating the power loss is expectedly large at low density and large current [1]}, [2]}. Consequently, carrier temperature rises with increasing current and decreasing carrier density, leading to dissipative transport in the channel, consistent with our experimental observations. The estimated dissipation rates indicate that the energy loss rate at \(I_{dc}=10~\mu \) A is of order 10\(^{-14}\)  W however, at 2 \(\mu \) A it is of order 10\(^{-16}\)  W, resulting in high carrier temperatures at large dc currents as reported in previous studies [1]}, [2]}. This estimate assumes a very rapid thermalization of the electrons on a time scale of few tens of femtoseconds, corroborated by recent experiments in graphene and related materials [5]}, [6]}
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